Question

If a star’s surface temperature is 30,000 K, how much power does a square meter of its surface radiate?

Answer 1

To calculate the emitted power per square meter we need to use Stefan-Boltzmann’s Law,
that is,

`E=sigmaT^4`,

where `E` = emitted power per square meter of surface

`T` = temperature in Kelvins

`sigma` = Stefan-Boltzmann's constant: `(5.670373xx10^(-8) "watt") /(1 "m"^2xxK^4)`

Given/Known:
`T="30000 K"`
area = `"1 m"^2"`
`sigma=(5.670373xx10^(-8) "watt")/(1"m"^2xx"K"^4")`
Unknown:
`E`

Solution:

`E=sigmaT^4=(5.670373xx10^(-8) "watt") /(1"m"^2xxcancel"K"^4)xx30000cancel"K"^4 = 5xx10^10 "watt/m"^2"`
(answer has 1 sig fig due to 1 sig fig in 30000K)

Resources:
http://astroweb.case.edu/ssm/100f09/HW4_soln.pdf
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law